The Mathematics of Politics

This book focuses on mathematical reasoning about politics. People commonly believe mathematics has nothing to say about politics. The high school experience suggests mathematics is the study of numbers, operations, formulas, and manipulations of symbols. Those who, from this experience, conclude mathematics has no relevance to politics will not

It is because mathematics is often misunderstood, it is commonly

believed it has nothing to say about politics. The high school

experience with mathematics, for so many the lasting impression

of the subject, suggests that mathematics is the study of numbers,

operations, formulas, and manipulations of symbols. Those

believing this is the extent of mathematics might conclude

mathematics has no relevance to politics. This book counters this impression.

The second edition of this popular book focuses on mathematical reasoning

about politics. In the search for ideal ways to make certain kinds

of decisions, a lot of wasted effort can be averted if mathematics can determine that

finding such an ideal is actually impossible in the first place.

In the first three parts of this book, we address the following three

political questions:

(1) Is there a good way to choose winners of elections?

(2) Is there a good way to apportion congressional seats?

(3) Is there a good way to make decisions in situations of conflict and

uncertainty?

In the fourth and final part of this book, we examine the Electoral

College system that is used in the United States to select a president.

There we bring together ideas that are introduced in each of the three

earlier parts of the book.

Autorentext

E. Arthur Robinson, Jr. is a Professor of Mathematics a Professor of mathematics at the George Washington University, where he has been since 1987. Like his coauthor, he was once the department chair. His current research is primarily in the area of dynamical systems theory and discrete geometry. Besides teaching the Mathematics and Politics course, he is teaching a course on Math and Art for the students of the Corcoran School the Arts and Design.

Daniel H. Ullman is a Professor of Mathematics at the George Washington University, where he has been since 1985. He holds a Ph.D. from Berkeley and an A.B. from Harvard. He served as chair of the department of mathematics at GW from 2001 to 2006, as the American Mathematical Society Congressional Fellow from 2006 to 2007, and as Associate Dean for Undergraduate Studies in the arts and sciences at GW from 2011 to 2015. He has been an Associate Editor of the American Mathematical Monthly since 1997. He enjoys playing piano, soccer, and Scrabble.

Inhalt

I VOTING

Two Candidates

Social Choice Functions

Criteria for Social Choice

Which Methods Are Good?

Arrow's Theorem

Variations on a Theme

Notes on Part I

II: APPORTIONMENT

Hamilton's Method

Divisor Methods

Criteria and Impossibility

The Method of Balinski and Young

Deciding among Divisor Methods

History of Apportionment in the United States

Notes on Part II

III CONFLICT

Strategies and Outcomes

Chance and Expectation

Solving Zero-Sum Games

Conflict and Cooperation

Nash Equilibria

The Prisoner's Dilemma

Notes on Part III

IV THE ELECTORAL COLLEGE

Weighted Voting

Whose Advantage?

Notes on Part IV

Solutions to Odd-Numbered Exercises and Problems